In the field of precision measuring instruments, devices are known for measuring said valve seats, for example from patent documents U.S. Pat. No. 5,533,384A, DD137970, EP2330378A1 and DE10121964B4. Such devices have an elongate shape defining a longitudinal axis, that is a shape that is elongated along such longitudinal axis, so as to be arranged to properly cooperate with the seat to be measured and are equipped with a sensor adapted to detect the profile of the tapered portion of the valve seat. In order to be able to scan the tapered portion of the valve seat in its length, the sensor must be able to radially move, for cooperating with areas of the tapered portion positioned at different distances from the seat axis. In this respect, the solution proposed by EP2330378A1 provides that the sensor is mounted on an oscillating element. However, this solution has the limitation of being not always sufficiently precise and reliable in terms of repeatability in the measurement and robustness. According to the solution described in DE10121964B4, the sensor is mounted on a slide movable along a guide, the latter being arranged parallel to the surface of the valve seat to be measured. The slide is moved by a motor having its axis of rotation aligned with the guide. Therefore, the device of DE10121964B4 has a portion that protrudes and is inclined, for example of an angle of 45 degrees, with respect to the longitudinal axis of the device. The slide with the respective sensor and the motor responsible for moving the slide are housed in the protruding and inclined portion. This solution has the disadvantage of making the device bulky. In particular, a ending portion of the device, at which the sensor is arranged, has a relatively large radial dimension that prevents the device to be used in particular operating conditions, for example, where the cylinder head including the valve seat to be measured is mounted on a support which defines a narrow passage, through which the device should be introduced to reach the valve seat.